{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<h1><center> Estimating Friedrich's coefficients describing the deterministic dynamics of Langevin model</center></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<center>Andreas W. Kempa-Liehr (Department of Engineering Science, University of Auckland)</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This notebooks explains the friedrich_coefficient features, which has been inspired by the paper of Friedrich et al. (2000): *Extracting model equations from experimental data*. Physics Letters A 271, p. 217-222"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The general idea is to assume a Langevin model for the dynamics of the time series $x(t)$ \n",
    "$$\\dot{x}(t) = h(x(t)) + \\mathcal{N}(0,R)$$\n",
    "with $\\dot{x}(t)$ denoting the temporal derivative, $h(x(t))$ the deterministic dynamics, and $\\mathcal{N}(0,R)$ a Langevin force modelled as Gaussian white noise with standard deviation $R$.\n",
    "Now, an estimate $\\tilde{h}(x)$ of the deterministic dynamics can be computed by averaging $\\dot{x}(t)$ for a specific interval $x(t)\\in[x-\\epsilon,x+\\epsilon]$ with $|\\epsilon|\\ll 1$:\n",
    "$$\\left.\\tilde{h}(x)\\right|_{x\\in[x-\\epsilon,x+\\epsilon]} \\approx \\frac{\\sum\\limits_{x(t)\\in[x-\\epsilon,x+\\epsilon]} x(t+\\Delta_t)-x(t)}{\\Delta_t \\sum\\limits_{x(t)\\in[x-\\epsilon,x+\\epsilon]} 1}.$$\n",
    "Having a set of estimations $\\{\\tilde{h}(x_1),\\tilde{h}(x_2),\\ldots,\\tilde{h}(x_n)\\}$ with $x_1<x_2<\\ldots<x_n$ at hand, Friedrich's coefficients are calculated by fitting a polynomial of order $m$ to these estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In order to demonstrate this approach, the dynamics of a dissipative soliton before and after its drift-bifurcation is simulated (Liehr 2013: *Dissipative Solitons in Reaction-Diffusion Systems*. Springer, p. 164).\n",
    "By applying the approach of Friedrich et al. for estimating the deterministic dynamics, the equilibrium velocity of the dissipative soliton is recovered.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/IPython/html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n",
      "  \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n",
      "/usr/local/lib/python2.7/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "from matplotlib import pylab as plt\n",
    "import numpy as np\n",
    "import seaborn as sbn\n",
    "import pandas as pd\n",
    "from tsfresh.examples.driftbif_simulation import velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from tsfresh.feature_extraction import ComprehensiveFCParameters\n",
    "from tsfresh.feature_extraction.feature_calculators import max_langevin_fixed_point, friedrich_coefficients\n",
    "settings = ComprehensiveFCParameters()\n",
    "default_params = settings['max_langevin_fixed_point'][0]\n",
    "default = settings['friedrich_coefficients']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def friedrich_method(v, param):\n",
    "    df = pd.DataFrame({'velocity': v[:-1,0], 'acceleration': np.diff(v[:,0])})\n",
    "    df['quantiles']=pd.qcut(df.velocity.values, 30)\n",
    "    groups = df.groupby('quantiles')\n",
    "    result = pd.DataFrame({'a_mean': groups.acceleration.mean(),\n",
    "                           'a_std': groups.acceleration.std(),\n",
    "                           'v_mean': groups.velocity.mean(),\n",
    "                           'v_std': groups.velocity.std()\n",
    "                          })\n",
    "    dynamics = friedrich_coefficients(v[:,0], param)\n",
    "    dynamics = [d[1] for d in dynamics]\n",
    "    v0 = max_langevin_fixed_point(v[:,0], **default_params)\n",
    "    \n",
    "    plt.subplot(2,1,1)\n",
    "    plt.plot(v[:,0])\n",
    "    plt.axhline(y=v0, color='r')\n",
    "    plt.xlabel('time')\n",
    "    plt.ylabel('velocity')\n",
    "\n",
    "    #Active Brownian motion is given if the linear term of the dynamics is positive\n",
    "    if dynamics[-2]>0:\n",
    "        active='Active'\n",
    "    else:\n",
    "        active=''\n",
    "        \n",
    "    plt.title('{} Brownian Motion (largest equilibrium velocity in red)'.format(active))\n",
    "    plt.subplot(2,1,2)\n",
    "    ax = plt.errorbar(result.v_mean,result.a_mean,\n",
    "                 xerr=result.v_std,fmt='o')\n",
    "    x = np.linspace(-0.004, 0.004, 201)\n",
    "    print(dynamics)\n",
    "    plt.plot(x, np.poly1d(dynamics)(x), label='estimated dynamics')\n",
    "    plt.plot(v0,0.,'ro')\n",
    "    plt.axvline(x=v0, color='r')\n",
    "    plt.xlabel('mean velocity')\n",
    "    plt.ylabel('mean acceleration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Beyond drift-bifurcation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ds = velocity(tau=3.8, delta_t=0.05, R=3e-4, seed=0)\n",
    "v = ds.simulate(1000000, v0=np.zeros(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-343.32787387478442, 0.037453057120062423, 0.0022569679511866667, -1.0236536382788926e-07]\n"
     ]
    },
    {
     "data": {
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4vV5qvV5SU6z74uo9O77W9otL9hGQwkV27S3n7hfn8OCkoO1q/Hj98zV8s3Ar738fFNi5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\nkxRWARljjEkKq4CMMcYkxf8DWO0VJNO8fCYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1152c3d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "friedrich_method(v, default)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Before drift-bifurcation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "ds = velocity(tau=2./0.3-3.8, delta_t=0.05, R=3e-4, seed=0)\n",
    "v = ds.simulate(1000000, v0=np.zeros(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-430.63544990116668, 0.083476393069130017, -0.0020234721659708023, 4.3026801890000346e-08]\n"
     ]
    },
    {
     "data": {
      "image/png": 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WKyBNWISjf2KxB70mftmZE9q8E18E+26Gs6vr6xEMqog1wS5QHA5aAUWY0rKK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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11565e150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "friedrich_method(v, default)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
